In accordance with the invention, a waveform having a harmonic structure closely approximating the sound of any given musical instrument may be readily produced by the expedient of selecting proper components to make up the waveform. Specifically, it has been found that conventional and easily produced square waves may be readily combined or otherwise manipulated to produce rectangular waves of selected frequencies and duty cycles. These rectangular waves may in turn be readily combined to produce a resultant waveform having virtually any desired harmonic structure. It can be confirmed by mathematical analysis that suitably selected and scaled rectangular waves of different duty cycles, when combined, result in waveforms having a harmonic content such that a highly accurate approximation of a given musical sound may be reproduced therefrom by conventional audio reproduction components.
The following detailed description is directed to one practical and preferred embodiment of the invention, wherein rectangular waves of selected duty cycle are produced by the combination of conventional square waves. These rectangular waves are then scaled in amplitude and combined to form a close approximation of a stair-step or sawtooth waveform, which may readily be filtered by conventional means to produce a resultant waveform having a desired harmonic content. It will be appreciated from the foregoing discussion, however, that the expedient of filtering is not strictly necessary, as the selection of rectangular waves of suitable duty cycles may be accomplished so as to form a resultant output waveform of desired harmonic structure, without filtering. However, it is believed preferable, as well as somewhat simpler, to initially produce a stair-step or sawtooth waveform, which is known to contain a full harmonic structure, and then to utilize conventional filters to remove or attenuate undesired harmonics, thus producing the desired harmonic structure in the resultant waveform. As will be seen in the following description, the number and identity of components utilized to accomplish the objects of the invention, in the preferred embodiment, are surprisingly simple, and yet considerably more accurate than any prior art structure or method of which we are aware, in producing the desired end results.
Electronic organs commonly are provided with the 12 semi-tones of the top octave of the organ. This may be done by means of 12 separate generators, or by means of a high frequency generator and 12 dividers of different divider ratio. These frequencies are applied to divide-by-two circuits to provide the remaining octaves of corresponding notes of the organ. Such division generally results in the production of square waves, i.e. rectangular waves of 50% duty cycle. Such waves are readily filtered to produce the flute tones, which are essentially sine waves with little or no harmonic structure. Such waves also produce remarkably good clarinet tones, but present problems with other tones, since square waves inherently present only an odd harmonic series, the even harmonics being lacking. It has been common practice to distort the square waves in keying, or to combine a plurality of square waves of multiple frequencies to approximate a staircase. The staircase, in turn, approximates a sawtooth wave which has (ideally) all of the harmonics present, whereby the wave may be filtered to produce substantially any desired type of instrumental tone. Unfortunately, such staircase waves are imperfect approximations, to the extent that some harmonics are missing or are of too low an amplitude to produce the desired sounds, when filtered.